Some results of S-transform analysis of the transient planetary-scale wind

Earth Planets Space, 51, 711–717, 1999
Some results of S-transform analysis of the transient planetary-scale wind
oscillations in the lower thermosphere
Yu. I. Portnyagin1 , E. G. Merzlyakov1 , Ch. Jacobi2 , N. J. Mitchell3 , H. G. Muller4 , A. H. Manson5 ,
W. Singer6 , P. Hoffmann6 , and A. N. Fachrutdinova7
1 Institute
for Experimental Meteorology, Obninsk, Russia
for Meteorology, University of Leipzig, Germany
3 Department of Physics, University of Wales, Aberystwyth, U.K.
4 Cranfield University, RMCS Shrivenham, Swindon, U.K.
5 Institute for Space and Atmospheric Studies University of Saskatchewan,, Saskatoon, Canada
6 Institute of Atmospheric Physics, Kuehlungsborn, Germany
7 Kazan State University, Kazan, Russia
2 Institute
(Received July 28, 1998; Revised February 8, 1999; Accepted April 20, 1999)
Technique appropriate to the analysis of lower thermospheric wind data recorded by global-scale networks of
ground-based instruments are discussed. The S-transform technique is shown to be effective in the analysis of the
main features of travelling planetary waves and this method is applied to the time series of horizontal-velocity data
obtained during the DYANA campaign (January-March, 1990). The analysis reveals strongly transient behavior of
the day-to-day lower thermosphere wind variations, as well as their specific longitudinal structure. In particular, it
was found that the revealed quasi-15 day and quasi-5 day wind oscillations may be described as transient westwardpropagating waves with zonal wavenumber s = 1, while an oscillation with the a period near 7 days is tentatively
identified as having a wavenumber s = 0.
1.
Introduction
that many members of the planetary-wave field in the lower
thermosphere exhibit significant variability on time scales
ranging from a few days to seasonal. In other words, the
wave activity displays nonstationary characteristics, i.e. its
spectral composition may change with time, and particular
wave modes can often be thought of as occurring in so-called
bursts or events of limited duration. Consequently, a
more sophisticated method of analysis is necessary to investigate on a global scale the occurrence, persistence, and
temporal variability of wind fluctuations with periods of a
few days to around 3 weeks. One such method of analysis of non-stationary wind fluctuations is the short-term
Fourier transform, discussed by Kamalabadi et al. (1997).
In the present work we demonstrate the application to the
global-scale analysis of lower-thermospheric wind data of
an alternative method, the S-transform, previously described
by Stockwell et al. (1996) and Fritts et al. (1998). In the
demonstration we use data from global-scale measurements
made in January-March 1990 as part of the DYANA (Dynamics Adapted Network) campaign. This type of data is
particularly timely in view of the global-scale observations
expected to be made as part of the PSMOS (Planetary-Scale
Mesopause Observing System) project.
Wind oscillations with periods in the range of 2 days to
a few weeks are frequently observed in the lower thermosphere (80–110 km). There is evidence that at least some
of these oscillations are global in nature and related to planetary waves, observed in the troposphere and stratosphere,
e.g. Vincent (1990). Following the initial work by Glass et
al. (1975), several attempts have been made to determine
the global scale structure of day-to-day lower thermosphere
wind oscillations: Muller and Nelson (1978), Craig et al.
(1983), Clark et al. (1994), Singer et al. (1994), Forbes et al.
(1995), Meek et al. (1996). It has been found that the most
frequently observed wind oscillations with periods near 2, 5,
10 and 16 days all correspond to predicted resonant frequencies of atmospheric disturbances associated with westwardpropagating Rossby normal modes.
To determine the amplitudes, phases and periods of such
waves from ground-based observations, the usual analysis
technique consists of applying standard spectral and harmonic methods, such as a Fourier or Lomb-Scargle periodogram analysis, to the recorded time series of wind data.
From the calculated phase differences between a number of
observing stations the zonal wave-number can be determined.
Usually it is precluded that during the period to be analyzed
the oscillation is stationary. However it is now well known
2.
Data Analysis
To demonstrate the proposed S-transform approach to the
of analysis of global scale winds we examined data obtained
during the DYANA campaign of January-March, 1990. From
this period we considered data in the form of hourly-mean
c The Society of Geomagnetism and Earth, Planetary and Space Sciences
Copy right
(SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan;
The Geodetic Society of Japan; The Japanese Society for Planetary Sciences.
711
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YU. I. PORTNYAGIN et al.: S-TRANSFORM ANALYSIS OF THE TRANSIENT PLANETARY-SCALE WIND OSCILLATIONS
winds, simultaneously measured by meteor-radar, MF-radar
and LF techniques in a rather narrow latitudinal belt at heights
between about 90–100 km. The locations and types of instruments used to record the data are given in Table 1. As it is
well known, each of these instruments have some limitations
in determination of the wind magnitudes, and this would give
a certain problem in determining the absolute amplitudes but
not the phases and periods. As to the amplitudes, our analysis is mainly confined the temporal variations of the relative
amplitudes.
The data have been analyzed to reveal the planetary scale
features in the day-to-day variations of the different wind
parameters. Two complementary methods of analysis were
used: firstly, the well-known periodogram and FFT spectral
analysis technique and, secondly, the S-transform technique.
The periodogram and spectral analysis were used to reveal
the main spectral components of the wind oscillations only.
In view of the anticipated transient nature of some of the
planetary waves, the S-transform technique offers a powerful insight into the spectral composition of the wind field.
The S-transform is closely related to the continuous wavelet
transform (CWT), and is in effect a phase correction of
the CWT, but its localizing function (a Gaussian) has nonzero mean (Stockwell et al., 1996, Fritts et al., 1998). The
advantages of this method lie in its direct connection to the
Fourier-transform, and the better temporal and frequency resolution compared to the short term Fourier transform. Also,
the S-transform permits determination of the absolutely referenced phase of a particular oscillation as a generalization
in the nonstationary processes (Stockwell et al., 1996).
In the present study, the hourly-mean wind data for each
station were first transformed to six hourly-mean wind data,
interpolated and filtered using a band-pass filter with the
high-frequency cut-off corresponding to a period of 2 days
and lower-frequency cut-off corresponding to a period of 50
days. To fill gaps in the time series we used a least-squares fitting of the neighboring values by second degree polynomial
with exponentially decreasing weights. The phase of a particular oscillation (calculated from the S-transform) at each
of the different instrument locations enables the corresponding longitudinal structure of the oscillation to be deduced.
Table 1. Data base.
Station
Latitude
Longitude
Sheffield
53 N
4W
MR∗
Kuehlungsborn
54◦ N
12◦ E
MR∗
Collm
52◦ N
15◦ E
LF
Obninsk
55◦ N
37◦ E
MR∗
Volgograd
49◦ N
44◦ E
MR∗
Kazan
56◦ N
49◦ E
MR
Saskatoon
∗
◦
52 N
:-station without height resolution.
◦
Method
◦
◦
107 W
MF
3.
Results and Discussion
The periodograms (not shown) calculated for each of the
stations reveal significant peaks which are consistent with
those derived elsewhere for the DYANA campaign by Singer
et al. (1994). It should be noted that, according to these
authors, the day-to-day variability observed in the recorded
winds at the stations in Western and Central Europe
(Sheffield, Kuehlungsborn, Juliusruh and Collm) was quite
similar. The stations in Eastern Europe (Obninsk, Volgograd
and Kazan) also revealed a similar wind variability with a
generally good correlation between the data for this region,
but a rather different pattern to those for the stations in Western and Central Europe, indicating a horizontal scale of about
1000 km for these variations.
Further evidence of the complex longitudinal structure of
the day-to-day variations, which are usually considered as a
manifestation of a planetary wave propagation in the lower
thermosphere, was obtained using the S-transform analysis
described above. Figures 1–4 present spectrograms of amplitude squared as a function of time and frequency derived by
this technique for the zonal and meridional winds recorded at
Saskatoon and Sheffield (Fig. 1), Kuehlungsborn and Collm
(Fig. 2), Obninsk and Kazan (Fig. 3) and Volgograd (Fig. 4).
The data set from each station used in the analysis had differing qualities (but the sum of the gaps didn’t cover greater
then 16% of a time series). So, to be sure that gaps present
in some of the data did not significantly contaminate the Stransform results, the S-transform was applied to the data
from Obninsk which had artificial data gaps deliberately inserted. The artificial gaps were placed at the same times as the
gaps found in the Kazan data and this resulted in that the contents of gaps has increased from 8% to 18% in the Obninsk
series. Comparison of the original and modified Obninsk
data (Figs. 3a) and 3b); 4c) and 4d)) shows that even with
the degraded data, the broad features of the spectrograms are
conserved. A comparison with the data from the relatively
nearby site at Kazan (Figs. 3c) and 3d)) reveals significant
differences in the spectral composition of the motion field
between these two sites and suggests that the discrepancies
represent genuine geophysical differences.
Inspection of Figs. 1–4 reveals a number of wave events
which appear at various time throughout the campaign period. The transient behavior of these oscillations, which have
periods typical of planetary waves, is markedly dissimilar
even over the comparatively narrow range of latitudes addressed in this study. However, some common features in
their temporal variations are apparent. In particular, during
the period of stratospheric warming (between about midJanuary and mid-February; day numbers 15–45) the spectra
are usually broader and the powers larger. Also, the most significant oscillations are present only in particular episodes or
wave events and for each station there are certain quiet
periods when no significant oscillations are observed. We
shall now consider particular features observed in the data.
A significant oscillation occurring with a period of about
13–15 days is clearly seen in both the zonal and meridional
components of the prevailing wind for all of the stations
under consideration. The time at which this oscillation attains maximum amplitude appears dependent on the longitude of the observation. The oscillation first appears over the
YU. I. PORTNYAGIN et al.: S-TRANSFORM ANALYSIS OF THE TRANSIENT PLANETARY-SCALE WIND OSCILLATIONS
713
Fig. 1. S-transform results of the measurements from Saskatoon (top) and Sheffield (bottom): a), c) zonal component; b), d) meridional component. The
scale is marked in units of amplitude-squared (m2 /s2 ).
Fig. 2. As for Fig. 1, but with measurements from Kuehlungsborn (top) and Collm (bottom): a), c) zonal component; b), d) meridional component.
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YU. I. PORTNYAGIN et al.: S-TRANSFORM ANALYSIS OF THE TRANSIENT PLANETARY-SCALE WIND OSCILLATIONS
Fig. 3. As for Fig. 1, but with measurements from Obninsk (top) and Kazan (bottom): a), c) zonal component; b), d) meridional component.
Fig. 4. As for Fig. 1, but with measurements from Volgograd (top) and Obninsk with artificial gaps (bottom): a), c) zonal component; b), d) meridional
component.
YU. I. PORTNYAGIN et al.: S-TRANSFORM ANALYSIS OF THE TRANSIENT PLANETARY-SCALE WIND OSCILLATIONS
Eastern European sites (Obninsk, Volgograd and Kazan) and
then over the Western and Central European sites (Sheffield,
Kuehlungsborn and Collm). However, the longitudinal dependence of the initial phase of this oscillation, presented in
Fig. 5a), shows a rather regular behavior. The slope of the fitted lines (determined by the least-squares method) is equal to
1.05 ± 0.17 for the zonal winds and 1.37 ± 0.2 for the meridional winds; and these lines are indicated in the figure. Both
of these slopes thus strongly indicate a westward-propagating
wave with zonal wavenumber s = 1. This oscillation may be
connected with the Doppler-shifted appearance of the well
known normal mode 16-day oscillation. Another possible
source of this oscillation is a hemispheric 13.8d oscillation,
propagating from below and apparently controlled by solar
activity as shown by Ebel et al. (1978). It is worth noting that
oscillations with a similar periods were also detected in temperature variations during the DYANA campaign (Bittner et
al., 1994). A comparison between the results of S-transform
and sliding least-squares fit for this wave is shown in Table 2
(the least-squares fit errors are shown in brackets). The initial
phases presented in this table were calculated at one middle
point for all stations. The columns time of max show the
moments (days), at which the wave’s amplitude attains its
maximum.
A second significant oscillation clearly revealed at the different longitudes is that with a period near 5 days. This
oscillation is apparent in both the zonal and meridional wind
data of Figs. 1–4, although it is more distinct in the meridional, rather than zonal component. This oscillation shows
an even more transient behaviour in comparison to the above
discussed 13–15 day oscillation. To investigate these oscillations in more detail we divided the data into groups of similar
apparent wave periods and time of appearance. This resulted
in consideration of a wave of period about 5.3 day in the data
from Obninsk and Kazan, and a wave with a period of about
4.3–4.4 days in the data from Sheffield and Saskatoon. For
each pair of sites the observed phases, presented in Fig. 5b),
correspond to a zonal wave numbers s = 1, but for Obninsk
and Kazan (slope is equal 1.29) this wave feature occurs before the main warming and for Sheffield and Saskatoon (slope
is equal 0.85) it occurs afterwards. The interval between the
observation of the wave at the two pairs of stations is equal
to about 20 days and during this interval the occurrence of
a warming distorts the 5-day wave, namely 3.7–4 days oscillations were observed around 12 February at Collm and
Kuehlungsborn. The DYANA campaign study of Bittner et
al. (1994) clearly revealed a nearly monochromatic temperature oscillation of about 5 days (4.2–6.5 days) and this wave
was observed at practically all stations. The related study
of Sheer et al. (1994) further investigated oscillations with
periods near to 5 days and concluded that a 5.8-day oscillation, revealed in the OH-rotational temperature measurements at Yakutsk (63◦ N, 130◦ ), Andoya (69◦ N, 16◦ E) and
Biscarrosse (44◦ N, 1◦ W) during the first part of the DYANA
campaign, has only two possible interpretations: namely, a
zonal wavenumber of either s = 1 or s = 2. However, a 4.7day oscillation observed during the second part of the campaign and documented at Yakutsk, Andoya and El Arenosillo
(37◦ N, 6◦ W) was found to be compatible with a westward
travelling wave of s = 4. The only alternative, wavenumber
715
Fig. 5. Phase distribution as a function of longitude for: a) The quasy-13-day
wave, solid squares—zonal component, open circles—meridional component; b) The quasy-5- day wave, meridional component only; c) 7-day
wave, meridional component only.
1, was not supported by the data at El Arenosillo. However
we may note that the latitude of this station is significantly
lower than for the other stations considered; and so to form
definite conclusions about the zonal wavenumber a more extended data set of winds/temperatures covering a wide range
of longitudes and times is needed.
In addition to the traveling planetary-scale oscillations
considered above, which are well known from theoretical
consideration, an unexpected meridional wind oscillation
with apparent zonal wavenumber s = 0 was revealed. The
period of this oscillation is near to 7 days and this disturbance (also rather transient in nature) has significant amplitudes (about 10 m/s) at the all considered measurement sites
with the exception of Saskatoon. The halfwidth of a signal, which modulates this wave amplitude is equals to about
11–13 days. The maximum amplitude of the 7-day wave is
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YU. I. PORTNYAGIN et al.: S-TRANSFORM ANALYSIS OF THE TRANSIENT PLANETARY-SCALE WIND OSCILLATIONS
YU. I. PORTNYAGIN et al.: S-TRANSFORM ANALYSIS OF THE TRANSIENT PLANETARY-SCALE WIND OSCILLATIONS
observed in the first week of February, but definitely earlier
for the Eastern stations. Figure 5c) represents the phase of
this oscillation as a function of longitude. The slope of the
fitted line is equal to −0.2 ± 0.07 at a significance level of
95%. This unusual feature appears similar to that reported
by Ebel et al. (1978), who observed a global scale wave with
the zonal wave number 0 and a period of about 7.5 days in
measurements of stratospheric total ozone, detected with the
space-born NIMBUS instruments.
The 95% significance levels of S-transform results were
calculated for each oscillation’s period separately. The level
was constructed with suggestion that a variance of a corresponding data raw is known. The variance was estimated for
the data raw without a trend and the tides. It is possible to
show that a peak of S-transform amplitude has const×χ 2 distribution if the data raw is a discrete realization of a gaussian
noise. Further we use a criteria like the Walker’s significance
test. A number of independent peaks for a fixed period of
wave is estimated as a ratio: the length of the analyzed data
raw/two wave’s period. The estimated 95% significance levels which correspond to wave’s periods 13–14, 6–7 and 4–5
day, are following: for wind components at Sheffield and
Kazan 4 m/s, 8 m/s, 11 m/s, respectively; at other stations
3 m/s, 6 m/s, 8.5 m/s. But it is worth to underline that the
observed waves have a tendency to gather in the groups of
simultaneous appearance. This grouping has very low probability for a random data set.
4.
Conclusions
The transient nature of planetary-wave oscillations in the
lower thermosphere have been revealed using the S-transform technique applied to ground-based radar wind measurements. Data recorded during the DYANA campaign reveals
the presence of quasi-15 days and quasi-5 days oscillations
which appear to be transient westward-propagating waves
with zonal wavenumber s = 1. Also observed during this
campaign was a transient oscillation with a period near to
7 days, tentatively identified as having a zonal wavenumber
s = 0. This study again demonstrates that for the PSMOS
campaigns the ground-based wind measurements, well distributed over the globe, are necessary.
Acknowledgments. The impetus for this work was given by Prof.
G. Shepherd. The authors are very grateful to him for his constant
attention and help in collecting of the data. This work was supported
in part by INTAS under grant 96-1669.
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